Very nice! You are eliminating the unnecessary parts of the circuit and soon you will be down to the bare Joule Thief that is lurking inside all of these circuits.
You will eventually reach the point where your LEDs are lit by the ambient power coming from any nearby radio transmitter or RF noise emitter. And then you will understand the secret of Akula/Ruslan/Wesley, and you will be well on the way to grokking Kapanadze as well.
http://www.youtube.com/watch?v=OgndINJHnd0
Could be

Nice demo

Except for 2 reasons that really aren't very strong reasons.
1) Lantern 4 operating condition is shown to be at kilo-hertz... but reviewing it, at that point of the board construction he has no LEDs, only the coil and drive circuit.
2) 3 5V LEDs in series requires more work than one 1.5V green LED... but the white LED type is not specified so they may also be low voltage...
But I'm not dismissin ya

My kacher version was working at 7Khz... don't know any radio sources at that range... (and then I searched and found... information at the end... )
I'm finding that the negative power field has interesting properties different from a positive potential; but I dunno... the resistor that makes more current... maybe because it holds that potential lower increasing the impedance, hence increasing the work needed to add to the field... touching my sphere-electrode .. increasing brightness and lowering power requirement... and it's not capacitance, adding a capacitor (tried multiple sizes) to any other point doesn't help, in fact hurts the performance... lots of 60Hz in the air, and touching a scope probe I can read like 100V from me... so maybe that's where it's coming from... hard to tell since I can't add a scope probe there and have it also work...
I do have faith that electrical engineers would never continue to work with a circuit that required touching it to make it work...
The thing the falstad sims gave me was that capacitors are not positive and negative as separate things, but moving charge to positive causes an inevitable flow of charge away from the other side immediately... So in the original schematic, even if positive is collected on the C28 cap, it ends up drawing in more from the ground side also... which means it's really a loop with the inductor anwyay... That's actually what breaks falstad simulator, if I end up with a condition that has current into both sides of a capacitor or away from both sides of a capacitor falstad fails immediately; LTSpice just gets really really slow trying to resolve the issue.
https://sites.google.com/site/somaliaamateurradio/somaliaphotos26"Here are some of the results of experiments on 0 – 9 kHz by amateur radio operators.
500 Hz – 5.000 kHz, 0.5 kHz – 5 kHz KC6QPO in the USA used 100 Watt Electric field to cover 3.3 km.
1.000 kHz, 1 kHz G3XBM in the UK used 4 Watts with ground electrodes (10 m base) to cover 0.3 km.
6.000 kHz, 6 kHz G0AKN in the UK used 1 kW (1000 Watts) with ground electrodes to cover 10 km.
6.000 kHz, 6 kHz KD4RLD in the USA used 100 watts with ground electrodes and loop to cover 10 km.
7.000 kHz, 7 kHz KD4RLD in the USA used 100 watts with ground electrodes and loop to cover 10 km.
8.800 kHz, 8.8 kHz KD4RLD in the USA used 100 watts with ground electrodes and loop to cover 10 km.
8.900 kHz, 8.9 kHz IW3SGT in Italy used 8 Watts to cover 0.1 km.
8.930 kHz, 8.93 kHz DK8KW in Germany used 10 Watts with Electric field to cover 1 km.
8.950 kHz, 8.95 kHz DJ2LF in Germany used 6 Watts with ground electrodes to cover 1.3 km.
8.950 kHz, 8.95 kHz DJ2LF in Germany used 14 Watts with Electric field to cover 2.5 km.
8.969 kHz, 8.969 kHz DF6NM in Germany used 20 Watts with a kite antenna to cover 4.5 km.
8.975 kHz, 8.975 kHz VK2ZTO in Australia used 380 Watts with ground electrodes to cover 1.6 km.
10.000 kHz, 10 kHz DL5KZ in Germany used 4 Watts from commercial equipment for finding underground cables with ground electrodes to cover 3 km.
Special license issued to radio amateurs in Germany to communicate on 8.9 kHz to 9 kHz.
Special license issued to radio amateurs in Sweden to communicate on 7 kHz to 8.5 kHz.
In some countries no license is needed to transmit below 9 kHz because internationally the frequencies from 0 – 9 kHz is not allocated to anyone."